Find the distance between points A and B, located on the opposite shores of a river, if on one of the shores following segments

Question

Ivanshal [37]

3 years ago

11

Find the distance between points A and B, located on the opposite shores of a river, if on one of the shores following segments

have been drawn and measured SB=60m, SC=80m, SD=180m and BC∥AD.

Mathematics

1 answer:

Gre4nikov [31] · Answer 1 · 2021-12-12T10:02:03+03:00

Gre4nikov [31]3 years ago

4 0

Answer:

AB= $75m$

Step-by-step explanation:

In the $\Delta SCB$ and $\Delta SDA$

$\angle S=\angle S\\BC||AD\\\Rightarrow\angle SBC=\angle SAD\\\angle SCB =\angle SDA$

$By\ AAA\ \Delta\ and\ \Delta SDA\ are\ similar\\\\ \Rightarrow\frac{SC}{SD} =\frac{SB}{SA} \\\\ \frac{80}{180} =\frac{60}{SA}\\\\ SA=60\times\frac{180}{80} \\\\SA=135\\\\AB=SA-SB\\\\=135-60\\\\=75m$